Parallel Sparse Approximate Inverse Preconditioning on Graphic Processing Units

Dehnavi, Maryam Mehri; Fernández, D.; Gaudiot, J.-L.; Giannacopoulos, Dennis D.

doi:10.1109/tpds.2012.286

Cited by 27 publications

(13 citation statements)

References 33 publications

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“…The performance of the matrix powers kernel in Krylov subspace methods will be studied and preconditioners such as the sparse approximate inverse [19] will be used to enhance the convergence of communication-avoiding KSMs.…”

Section: Discussionmentioning

confidence: 99%

Communication-Avoiding Krylov Techniques on Graphic Processing Units

et al. 2013

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Communicating data within the graphic processing unit (GPU) memory system and between the CPU and GPU are major bottlenecks in accelerating Krylov solvers on GPUs. Communication-avoiding techniques reduce the communication cost of Krylov subspace methods by computing several vectors of a Krylov subspace "at once," using a kernel called "matrix powers." The matrix powers kernel is implemented on a recent generation of NVIDIA GPUs and speedups of up to 5.7 times are reported for the communication-avoiding matrix powers kernel compared to the standards prase matrix vector multiplication (SpMV) implementation.

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Section: Discussionmentioning

confidence: 99%

Communication-Avoiding Krylov Techniques on Graphic Processing Units

et al. 2013

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“…Table shows NVIDIA GPUs that are used in the performance evaluation. The test matrices are selected from the University of Florida Sparse Matrix Collection, and have been widely used in some previous work . Table summarizes the information of the sparse matrices, including the name, kind, dimension, and total number of nonzeros.…”

Section: Evaluation and Analysismentioning

confidence: 99%

“…This feature is quite attractive especially from the point of view of a parallel implementation on the GPU architecture because this type of mathematical operation inherently involves a high level of concurrency . Furthermore, FSAI preconditioners can fail due to breakdowns during an incomplete factorization process . A comparative study of various approximate inverse preconditioners was presented in the work of Benzi and Tuma .…”

Section: Introductionmentioning

confidence: 99%

An efficient sparse approximate inverse preconditioning algorithm on GPU

Yin

Gao

2019

Concurrency and Computation

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Summary The sparse approximate inverse (SPAI) preconditioner has proven to be effective in accelerating the convergence of iterative methods. Recently, accelerating it on the graphics processing unit (GPU) has attracted considerable attention due to the fact that the cost of constructing it is high. This motivates us to investigate how to accelerate the construction of SPAI preconditioners on GPU in this paper. We propose an efficient sparse approximate inverse algorithm on GPU, called SPAI‐Adaptive. For our proposed SPAI‐Adaptive, there are the following novelties: (1) an adaptive thread allocation strategy for SPAI‐Adaptive is proposed to assign the optimal thread number for each column of the preconditioner, and (2) Each component of the preconditioner, which includes finding indices I and J, constructing local submatrix, decomposing the local matrix into QR, and solving the upper triangular linear system, is computed in parallel inside a thread group of GPU. Experimental results show that the proposed SPAI‐Adaptive is effective, and has good performance and high parallelism.

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“…When testing the bilinear form solver, SAI is used instead to precondition both BiCG and GMRES. SAI is considered a weak preconditioner, yet due to its exceptional parallel properties has been rediscovered in recent years and gained popularity as a GPU preconditioning strategy [32]. Since the true inverse of a sparse matrix is often dense, it is necessary to select an initial non-zero pattern for SAI.…”

Section: Preconditioningmentioning

confidence: 99%

Improved Functional-Based Error Estimation and Adaptation without Adjoints

Tyson

Swirydowicz

Derlaga

et al. 2016

46th AIAA Fluid Dynamics Conference

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Adjoint methods have become the state of the art in recent years for both functional error estimation and adaptation. But, since most engineering applications rely upon multiple functionals to assess a physical process or system, an adjoint solution must be obtained for each functional of interest which can increase the overall computational cost significantly. In this paper, new techniques are presented for functional error estimation and adaptation which provide the same error estimates and adaptation indicators as a conventional adjoint method, but do so much more efficiently, especially when multiple functionals must be examined. For functional error estimation, the adjoint solve is replaced by the solution of an error transport equation for the local solution error and an inner product with the functional linearization. This method is shown to produce the same functional error estimate as an adjoint solve. For functional-based adaptation, the bilinear form of the adjoint correction to the functional is exploited in a manner so as to obtain the adjoint variables in an approximate sense but still accurate enough to form useful adaptation indicators. These new methods for functional error estimation and adaptation are tested using the quasi-1D nozzle problem.

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Parallel Sparse Approximate Inverse Preconditioning on Graphic Processing Units

Cited by 27 publications

References 33 publications

Communication-Avoiding Krylov Techniques on Graphic Processing Units

Communication-Avoiding Krylov Techniques on Graphic Processing Units

An efficient sparse approximate inverse preconditioning algorithm on GPU

Improved Functional-Based Error Estimation and Adaptation without Adjoints

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